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At Hanover, students’ growth in math fostered by collaborative learning

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MERIDEN — The math block had just begun in Alyse Hogan’s fourth grade classroom at Hanover Elementary School on Thursday morning. 

Hogan pointed to the board and asked students, who at that point were still seated in their desks, to read aloud with her the problem of the day. Together, they read through that problem, which involved long division, three times.

Every time Hogan’s students read through the problem, she would follow with questions that would get them thinking about what they were being asked to solve. Students would need to determine how to go about doing so.

In this problem, students had to determine how many bags a fictional person named Bryce would need, to evenly distribute 64 prizes. Bryce was limited to three prizes per bag. 

“What’s he doing? … What task are we going to be focused on?” Hogan asked, as students raised their hands in response. “How many bags will we have? What do we need to know from the problem here to get the answer?”

With that, students quickly assembled into groups of three, with a person in each group grabbing a white board, marker and eraser. They scattered throughout the room, placed the whiteboards vertically on top of desks, leaning them slight against their classroom wall and window. They went straight to work. 

Chatter in the room grew, as students huddled around their boards and talked their way through the problem, passed their markers back and forth, and took turns writing out their solutions. 

Hogan walked down the center of the room and watched as students employed different strategies to the problem. Down the hall, in Susan Soroka’s fourth grade classroom, a similar scene played out. 

A new math block

Several years ago, Meriden Public Schools as a district shifted its approach to teaching elementary school math. So Hanover and other city elementary schools adopted 90-minute math blocks into their daily schedules, with the time carved out within that block for students to collaborate in group problem solving.

The shift has already shown promising results, with students showing strong math gains across all schools. Greater numbers of students reached their math targets on the statewide Smarter Balanced Assessment student achievement texts, in the spring of 2022 compared to 2019. 

In 2020, due to the COVID-19 pandemic, testing did not take place that year. The following spring, 2021, testing resumed, but results were not used for school accountability purposes. 

Results reported from last spring showed all schools made gains, with Hanover showing the largest growth. In 2019, 67% of Hanover students reached their growth targets. Three years later, that percentage jumped 17 points to 84%, according to figures shared by the Meriden Public Schools. 

This year, at Hanover, fourth grade teachers like Hogan and her colleague Susan Soroka decided to expand upon the small group approach honed in their extended math blocks — bringing what educators have coined as “vertical workstations” into their classrooms. The idea came from a book, called “Building Thinking Classrooms,” that Hanover staff had read over the summer. 

The approach Hogan and Soroka adopted requires students to collaborate, to verbally explain their thinking and to show their work. As educators explained, students must not only calculate a solution to the problem, every member of each group also needs to be able to explain how they solved it. 

In Hogan’s classroom Bryson Batista, Emily Terribile and Jesse Torres decided to tackle the problem through a model called “The Big 7.” It consists of using partial quotients to solve a problem. 

Their chain of arithmetic ran down their board. The trio were close to solving the problem: 21 bags with a remainder of one prize. 

“I think the last one we should do is two times three, right?” Torres asked his peers.

Terribile observed they have a remainder. “So he will have one for himself,” she said.

After it was clear that each of them agreed on the solution and how they reached it, they signaled to their teacher they had completed the task. Their peers around the room would similarly wrap up.

But they were not yet done. Hogan went around the room, asking members of each group to share their thinking with all of their classmates.

Students learn the most from their peers

The approach the teachers adopted is based on educational research that shows students learn best from each other, Hogan explained. Having them share a vertical work surface and not use worksheets helps keep students engaged.

“Students should be sharing the marker. The idea is for them to be sharing their thinking, sharing their different approaches,” Hogan said.

The new approach required some adjustments at first. Hogan and Soroka are already seeing results.  

“It’s always interesting to see the different approaches they take,” Hogan said. For example, some students might use the Big 7, or another method called the area model, to solve the problem. 

“We all think in different ways,” Hogan said. Regardless of the strategy students opt to use, the “main goal is to get them thinking.”

It required a little bit of letting go on the part of their teacher. 

“Because you want to show them. You want them to get the answer right, you might want them to try exactly what you showed them that day, because that’s what you have in your mind,” Hogan said. “But if they’re not doing the thinking, it doesn’t matter. The wheels need to be turning for them. Whether they get the right answer or not.”

Soroka said the approach allows students to “truly understand what the meaning of division is and what they’re doing.”

“They’re doing it in different ways and getting the same answer – because not everybody’s brain works the same,” Soroka said. 

Developing a deeper understanding of math is not the only goal.  

“They’re learning how to work with others,” Soroka said. 

“They seemed to be more willing to do the hard thinking,” Hogan said separately.

Orlando Valentin, Hanover’s assistant principal, reiterated what Hogan and Soroka explained about the effectiveness of small group learning. 

“It seems loud and busy, but the kids are having math talk,” Valentin said. “We know that getting kids in small groups, getting them to use math vocabulary and to talk with their peers does have results.”

A part of those discussions is what staff called error analysis. If a group does not arrive at the correct solution, they and their classmates review the steps to see where the error was made. 

Hanover Principal Jennifer Kelley called that review and reflection “authentic learning.”

“When you find a mistake you made, when you go back and reflect on it, you learn oh, ‘it was because I did this’ — that’s authentic learning,” Kelley said. 

While it can be frustrating for their students to not arrive at the correct solution, educators also encourage them to not get discouraged.

Daniel Crispino, director of school leadership for the city’s elementary schools, described the overall approach as “another way to get kids to engage in conversation, using high-quality vocabulary and having that productive struggle.”

Crispino said other schools have taken similar approaches, in having students working in groups. In terms of students’ academic progress, Crispino said at this point students appear to be several months ahead in their learning, than they were a year prior.

He praised teachers like Hogan and Soroka.

“Our teachers have realized great ways to implement their own ideas,” Crispino said, adding he is “blown away by the engagement, math vocabulary and student excitement — without fear of failure.”

“When you can do those things, you can be successful,” Crispino said. 



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